# Math Help - Cocky UPenn student throughs down challenge

1. ## Cocky UPenn student throughs down challenge

Draw an isosceles triangle ABC with Side AB = Side AC. Draw a line from C to side AB and label that line CD. Now draw a line from B to side AC. Label that line BE. Let angle EBC = 60 degrees, angle BCD equal 70 degrees, angle ABE equal 20 degrees, and angle DCE equal 10 degrees. Now draw line DE.

Find what angle EDC is by using geometry only and no trigonometry.

Don't cheat and use protractors/rulers/all that stuff either! Go by pure geometric reasoning
This is a tedious drawing so if you are going to procede I'll thank you in advance. Here is my reasoning for solving this problem.

Call the intersection of BE and CD point M. Let ADE=x, EDM=y, DEA=z, and DEM=140-z.

Thus we have the following system of equations:

(x+y)+20+10=180
x+20+z=180
50+y+(140-z)=180

And when I solve this I get a large angle, a negative angle, and an angle of zero. I think my work is sound. Please look it over.

Thanks

2. Try searching the internet for Langley's Problem. It is similar-I solved it some time ago using trigonometry.

3. Thanks. This is very similar. If you have time though or if someone else does, I'd appreciate it if it would be possible to look over my work. I'll try to include a diagram, but I think I haven't made any errors.

4. Originally Posted by Jameson
Thanks. This is very similar. If you have time though or if someone else does, I'd appreciate it if it would be possible to look over my work. I'll try to include a diagram, but I think I haven't made any errors.
Not necessarily you made a mistake, but the determinant of this system is zero. Because the matrix's diagnol is filled with zeros.

5. Then I need to find a way to set a system with a non-zero determinant. Hmmm... any ideas? I'm only missing four angles on this diagram.

6. Originally Posted by Jameson
Then I need to find a way to set a system with a non-zero determinant. Hmmm... any ideas? I'm only missing four angles on this diagram.
This problem is not designed to be treated as a high-school angle solving problem. The trick it to draw a contrusction and even from there it is difficult.
BTW if your system is consistent, then all solutions can be expressed though a parameter $t$. Then all you need to to find a solution that is 'reasonable' since there are infinitely many.

7. hmm, i'll work on it

8. is it 60????

EDIT: ok, nevermind that's wrong.

9. The answer is 20. The question was asked on www.collegeconfidential.com on the UPenn forum, and the OP hasn't posted an explanation to the solution to this problem. Here is a link that will guide you though. http://agutie.homestead.com/files/LangleyProblem.html